Mathematical modelling, a supercomputer and massively parallel computer technology will be used to investigate basic electrophysiological processes involved in the initiation and propagation of the mammalian cardiac impulse, both under normal conditions and during disease states. Models of single atrioventricular (AV) nodal, Purkinje and ventricular cells will be used to perform numerical simulations for the study of complex non-linear dynamics and chaotic behavior. In single cell models, we will test the hypothesis that periodic rate-dependent activations patterns in single cardiac cells are a consequence of a non-linear recovery of excitability during diastole, and will develop an analytical model of excitability based on the recovery kinetics and voltage-dependence of the appropriate transmembrane currents, in an attempt to predict the precise dynamics of rate-dependent activation of single cardiac cells. We will also investigate the non-linear dynamics of propagation in one and two- dimensionally connected bundles of AV nodal cells, linear Purkinje fibers and branching Purkinje networks. We will study the influence of varying the regenerative properties of the individual elements, or the degree of electrical interaction among them. Localized zones of depressed conduction separating regions of normal activity will also be created by high resistance coupling and/or by low excitability, to test the hypothesis that rate-dependent conduction block is a result of the discontinuities in cell excitability, geometrical arrangements of cell-to-cell connections and/or electrical coupling. We will also analyze the response of these models to repetitive stimulation on the basis of the theory of dynamical systems (chaos theory), with particular attention paid to amplification or reduction of local beat-to-beat changes in activation parameters (e.g., latency, action potential duration, etc.) by propagation. The nature of propagation in isotropic and anisotropic ventricular muscle will be studied in models of one-and two-dimensional arrays of ventricular cells coupled through gap junctions. The interplay between intercellular coupling resistance an membrane generator properties, and their effects on conduction velocity and patterns of propagation will be investigated systematically. Further, we will determine whether functional block and circuitous pathways can be generated in these two-dimensional models as a consequence of the nonuniform anisotropic distribution of axial resistivity, and whether reentry requires a critical relationship between relative size and orientation of the region of block and the curvature of the wavefront reaching that region. Predictions from the simulations will be compared with experimental results obtained in other projects and model predictions will be used to design further biological experiments. Overall, the simulations will be used to probes the underlying cellular mechanisms of normal and abnormal heart rate and rhythm.